Meanwhile, Ban hosted a closed-door banquet in Park's honor at his official residence soon after Park arrived in New York for the U.N. General Assembly on Friday.

The two met each other on several occasions during the U.N.

sessions. In the session on South Korea's "Saemaeul Movement," or new community movement, Ban said he was moved as U.N. member states adopted and carried out the movement for the first time in the history of the U.N.

The initiative -- launched by Park's father, then-President Park Chung-hee, in the 1970s -- is credited with helping modernize the then-rural South Korean economy.

Ban also said the Saemaeul Movement spread in countries ranging from Asia to Africa "like a forest fire."

He also expressed gratitude to Park for sharing South Korea's development know-how with developing countries.

Park smiled and clapped her hands after Ban's speech and told him "thanks" in Korean.

Ban also vowed to assist in efforts to promote peace and the development of inter-Korean relations, a key agenda of Park.

The apparent rapport between the two leaders and Ban's active support of Park in the U.N. may rekindle the rumor of Ban's possible candidacy, despite his objection to getting involved in South Korea's domestic politics.

Ban's second five-year term at the U.N. is set to end at the end of 2016, a year before South Koreans go to the polls to elect a new president who will replace Park.

Park's single five-year term ends in early 2018, and by law, she cannot seek re-election. (Yonhap)